离散数学
The Shortest Superstring Problem (SSP) consists, for a set of strings S = {s_1,...,s_n}, to find a minimum length string that contains all s_i, 1 <= i <= k, as substrings. This problem is proved to be NP-Complete and APX-hard. Guaranteed…
We propose a generic algorithm for computing the inverses of a multiplicative function under the assumption that the set of inverses is finite. More generally, our algorithm can compute certain functions of the inverses, such as their power…
Let $G(n,\, M)$ be the uniform random graph with $n$ vertices and $M$ edges. Let $B_n$ be the maximum block-size of $G(n,\, M)$ or the maximum size of its maximal $2$-connected induced subgraphs. We determine the expectation of $B_n$ near…
Despite its long history, the classical game of peg solitaire continues to attract the attention of the scientific community. In this paper, we consider two problems with an algorithmic flavour which are related with this game, namely…
The deterministic random walk is a deterministic process analogous to a random walk. While there are some results on the cover time of the rotor-router model, which is a deterministic random walk corresponding to a simple random walk,…
Let $G=(V,E)$ be a finite undirected graph. An edge set $E' \subseteq E$ is a dominating induced matching (d.i.m.) in $G$ if every edge in $E$ is intersected by exactly one edge of $E'$. The Dominating Induced Matching (DIM) problem asks…
In this paper we consider a layered-security model in which the containers and their nestings are given in the form of a rooted tree $T$. A {\em cyber-security model\/} is an ordered three-tuple $M = (T, C, P)$ where $C$ and $P$ are…
A random jigsaw puzzle is constructed by arranging $n^2$ square pieces into an $n \times n$ grid and assigning to each edge of a piece one of $q$ available colours uniformly at random, with the restriction that touching edges receive the…
A \emph{biclique} is a maximal bipartite complete induced subgraph of $G$. Bicliques have been studied in the last years motivated by the large number of applications. In particular, enumeration of the maximal bicliques has been of interest…
The topic of the article is the parametric study of the complexity of algorithms on arrays of pairwise distinct integers. We introduce a model that takes into account the non-uniformness of data, which we call the Ewens-like distribution of…
Path-addition is an operation that takes a graph and adds an internally vertex-disjoint path between two vertices together with a set of supplementary edges. Path-additions are just the opposite of taking minors. We show that some classes…
A matching $M$ in a graph $G$ is said to be uniquely restricted if there is no other matching in $G$ that matches the same set of vertices as $M$. We describe a polynomial-time algorithm to compute a maximum cardinality uniquely restricted…
Here we show that by expressing a van der Waerden number $W(r, k)$ by its radix polynomial representation, it not only is possible to locate each proper subset on $\mathbb{R}$ in which the van der Waerden number lies, but also to show that…
This article analyzes directed lattice paths, when a boundary reflecting or absorbing condition is added to the classical models. The lattice paths are characterized by two time-independent sets of rules (also called steps) which have a…
It is known that there are no more Lyndon words of length n than there are periodic necklaces of same length. This paper considers a similar problem where, additionally, the necklaces must be without some forbidden factors. This problem…
The celebrated Cheeger's Inequality establishes a bound on the edge expansion of a graph via its spectrum. This inequality is central to a rich spectral theory of graphs, based on studying the eigenvalues and eigenvectors of the adjacency…
An $N$-superconcentrator is a directed, acyclic graph with $N$ input nodes and $N$ output nodes such that every subset of the inputs and every subset of the outputs of same cardinality can be connected by node-disjoint paths. It is known…
The theory of combinatorial designs has recently been used in order to build switch-centric data centre networks incorporating a large number of servers, in comparison with the popular Fat-Tree data centre network. The construction…
Let I be an independent set of a graph G. Imagine that a token is located on any vertex of I. We can now move the tokens of I along the edges of the graph as long as the set of tokens still defines an independent set of G. Given two…
Gy{\'a}rf{\'a}s et al. and Zaker have proven that the Grundy number of a graph $G$ satisfies $\Gamma(G)\ge t$ if and only if $G$ contains an induced subgraph called a $t$-atom.The family of $t$-atoms has bounded order and contains a finite…